A130910 Sum {0<=k<=n, k mod 16} (Partial sums of A130909).

0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 120, 121, 123, 126, 130, 135, 141, 148, 156, 165, 175, 186, 198, 211, 225, 240, 240, 241, 243, 246, 250, 255, 261, 268, 276, 285, 295, 306, 318, 331, 345, 360, 360, 361, 363, 366, 370, 375, 381, 388

Offset: 0

Author

Hieronymus Fischer, Jun 11 2007

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A130486, A010872, A010873, A010874, A010875, A010876, A010878, A130481, A130482, A130483, A130484, A130485, A130487.

Programs

Mathematica

Accumulate[Mod[Range[0,60],16]] (* Harvey P. Dale, May 30 2020 *)

Formula

a(n)=120*floor(n/16)+A130909(n)*(A130909(n)+1)/2. - G.f.: g(x)=(sum{1<=k<16, k*x^k})/((1-x^16)(1-x)). Also: g(x)=x(15x^16-16x^15+1)/((1-x^16)(1-x)^3).

a(n) = +a(n-1) +a(n-16) -a(n-17). G.f. ( x*(1 +2*x +3*x^2 +4*x^3 +5*x^4 +6*x^5 +7*x^6 +8*x^7 +9*x^8 +10*x^9 +11*x^10 +12*x^11 +13*x^12 +14*x^13 +15*x^14) ) / ( (1+x) *(1+x^2) *(1+x^4) *(1+x^8) *(x-1)^2 ). - R. J. Mathar, Nov 05 2011