Linear Recurrence Nth Term Calculator
Calculate a distant term of a constant-coefficient linear recurrence, optionally modulo a whole modulus.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Exponentiate the companion matrix by repeated squaring; normalize modular arithmetic at every operation.
Companion-matrix state at n = M^(n−order+1)×reversed initial state
Worked example
Coefficients 1,1 and initials 0,1 define Fibonacci numbers, giving a[10]=55 and a[11]=89.
Assumptions and input details
1–8 coefficients with the same initial count. Modular inputs must be whole; ordinary arithmetic is floating-point and may lose integer exactness or exceed range. No symbolic closed form or arbitrary-precision nonmodular result is supplied.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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