A082206 Digit sum of A082205(n).
1, 4, 7, 10, 11, 14, 17, 18, 21, 24, 25, 28, 31, 32, 35, 38, 39, 42, 45, 46, 49, 52, 53, 56, 59, 60, 63, 66, 67, 70, 73, 74, 77, 80, 81, 84, 87, 88, 91, 94, 95, 98, 101, 102, 105, 108, 109, 112, 115, 116, 119, 122, 123, 126, 129, 130, 133, 136, 137, 140, 143, 144
Offset: 1
Examples
The first six palindromes are 1, 22, 232, 3223, 22322, 232232.
Links
- G. C. Greubel, Table of n, a(n) for n = 1..5000
- Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
Programs
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Magma
R
:=PowerSeriesRing(Integers(), 70); Coefficients(R!( (1+3*x+3*x^2+2*x^3-2*x^4)/((1-x)*(1-x^3)) )); // G. C. Greubel, Jan 22 2024 -
Mathematica
CoefficientList[Series[(1+3x+3x^2+2x^3-2x^4)/((1-x)*(1-x^3)),{x,0,70}],x] (* Vladimir Joseph Stephan Orlovsky, Jan 26 2012 *) Join[{1},LinearRecurrence[{1, 0, 1, -1},{4, 7, 10, 11},61]] (* Ray Chandler, Aug 25 2015 *) -
SageMath
def a(n): # a = A082206 if n<5: return 3*n-2 else: return a(n-3) + 7 [a(n) for n in range(1,71)] # G. C. Greubel, Jan 22 2024
Formula
For n>1, a(n+3) = a(n) + 7.
G.f.: x*(1 + 3*x + 3*x^2 + 2*x^3 - 2*x^4)/((1-x)*(1-x^3)). - Vladimir Joseph Stephan Orlovsky, Jan 26 2012
a(n) = -a(n-1) - a(n-2) + 7*(n-1), for n >= 4, with a(n) = 3*n-2 for n < 4. - G. C. Greubel, Jan 22 2024
Extensions
Edited by Don Reble, Mar 13 2006
Offset corrected by Mohammed Yaseen, Aug 15 2023