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

1,2

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).

Formula

For n>1, a(n+3) = a(n) + 7.

a(n) = A007953(A082205(n)).

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

Example

The first six palindromes are 1, 22, 232, 3223, 22322, 232232.

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 *)

Prog

(Magma) R<x>:=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
(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

Crossrefs

Cf. A007953, A047342, A082204, A082205.

Sequence in context: A370759 A223024 A275340 * A115566 A364840 A190507

Adjacent sequences: A082203 A082204 A082205 * A082207 A082208 A082209

Keyword

base,easy,nonn,less

Author

Amarnath Murthy, Apr 10 2003

Extensions

Edited by Don Reble, Mar 13 2006

Offset corrected by Mohammed Yaseen, Aug 15 2023

Status

approved