A289992 Number of magic labelings of the prism graph I X C_8 having magic sum n.

1, 49, 746, 6122, 34067, 144963, 506772, 1524628, 4074949, 9898229, 22220990, 46695870, 92769495, 175610631, 318756136, 557659432, 944355593, 1553488697, 2489980818, 3898657938, 5976186139, 8985711691, 13274641084, 19296041660, 27634190285

Offset

0,2

Links

Table of n, a(n) for n=0..24.

R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973. [Cached copy, with permission]

Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Formula

a(n) = A244880(n) + 2*Sum_{i=0..n-1} A244880(i).

From Colin Barker, Sep 13 2017: (Start)

G.f.: (1 + x)*(1 + 6*x + x^2)*(1 + 32*x + 70*x^2 + 32*x^3 + x^4) / (1 - x)^10.

a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>9. (End)

[Proof of the g.f. follows from the convolution formula and insertion of the g.f. A244880(x): Sum_{n>=0} a(n)x^n = Sum_{n>=0} A244880(n)*x^n +2*Sum_{n>=0} Sum_{i=0..n-1} A244880(i)*x^n = A244880(x) +2*Sum_{i>=0} Sum_{n>=i+1} A244880(i)*x^n = A244880(x) +2*Sum_{i>=0} A244880(i)*x^(i+1) Sum_{n>=0} x^n = A244880(x)+2*A244880(x)*x/(1+x) = A244880(x)*(1+2*x/(1-x)). R. J. Mathar, Mar 09 2025]

Crossrefs

Cf. A019298, A061927, A244497, A292281, A244873, A244880.

Sequence in context: A175775 A215117 A350982 * A357653 A278284 A110906

Adjacent sequences: A289989 A289990 A289991 * A289993 A289994 A289995

Keyword

nonn,easy

Author

David J. Seal, Sep 13 2017

Status

approved