A353974 a(n) is the n-th partial sum of A056992.

0, 1, 5, 14, 21, 28, 37, 41, 42, 51, 52, 56, 65, 72, 79, 88, 92, 93, 102, 103, 107, 116, 123, 130, 139, 143, 144, 153, 154, 158, 167, 174, 181, 190, 194, 195, 204, 205, 209, 218, 225, 232, 241, 245, 246, 255, 256, 260, 269, 276, 283, 292, 296, 297, 306, 307, 311

Offset: 0

Author

Stefano Spezia, May 12 2022

Keywords

• nonn
• base
• easy

Comments

Also the n-th partial sum of the main diagonal of A353109, or equivalently, the trace of the matrix M(n) whose permanent is A353933(n) for n > 0.

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,1,-1).

Crossrefs

Cf. A003991, A010888, A056992, A071317, A353109, A353933.

Programs

Mathematica

CoefficientList[Series[x(1+4x+9x^2+7x^3+7x^4+9x^5+4x^6+x^7+9x^8)/((1-x)^2(1+x+x^2)(1+x^3+x^6)),{x,0,56}],x]

Formula

G.f.: x*(1 + 4*x + 9*x^2 + 7*x^3 + 7*x^4 + 9*x^5 + 4*x^6 + x^7 + 9*x^8)/((1 - x)^2*(1 + x + x^2)*(1 + x^3 + x^6)).

a(n) = a(n-1) + a(n-9) - a(n-10) for n > 9.

a(n) ~ 51*n/9.