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

0,3

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

Table of n, a(n) for n=0..56.

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

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.

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]

Crossrefs

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

Sequence in context: A143707 A306989 A003248 * A071317 A167201 A336145

Adjacent sequences: A353971 A353972 A353973 * A353975 A353976 A353977

Keyword

nonn,base,easy

Author

Stefano Spezia, May 12 2022

Status

approved