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

Author

Amarnath Murthy, Apr 10 2003

Keywords

• base
• easy
• nonn
• less
• changed

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).

Crossrefs

Cf. A007953, A082204, A082205.

Essentially the same as A047342.

Programs

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.

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

Extensions

Edited by Don Reble, Mar 13 2006

Offset corrected by Mohammed Yaseen, Aug 15 2023