A244869 Number of magic labelings with magic sum n of first graph shown in link.

1, 9, 43, 143, 379, 859, 1738, 3226, 5597, 9197, 14453, 21881, 32095, 45815, 63876, 87236, 116985, 154353, 200719, 257619, 326755, 410003, 509422, 627262, 765973, 928213, 1116857, 1335005, 1585991, 1873391, 2201032, 2573000, 2993649, 3467609, 3999795, 4595415, 5259979, 5999307, 6819538

Offset

0,2

Links

Colin Barker, Table of n, a(n) for n = 0..1000

N. J. A. Sloane, Graphs for A244869-A244876.

R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]

Index entries for linear recurrences with constant coefficients, signature (5,-9,5,5,-9,5,-1).

Formula

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

From Colin Barker, Jan 11 2017: (Start)

a(n) = (15*(63 + (-1)^n) + 2592*n + 2880*n^2 + 1660*n^3 + 510*n^4 + 68*n^5) / 960.

a(n) = 5*a(n-1) - 9*a(n-2) + 5*a(n-3) + 5*a(n-4) - 9*a(n-5) + 5*a(n-6) - a(n-7) for n>6.

(End)

Mathematica

LinearRecurrence[{5, -9, 5, 5, -9, 5, -1}, {1, 9, 43, 143, 379, 859, 1738}, 50] (* Paolo Xausa, Dec 06 2023 *)

Prog

(PARI) Vec((1+4*x+7*x^2+4*x^3+x^4) / ((1-x)^6*(1+x)) + O(x^40)) \\ Colin Barker, Jan 11 2017

Crossrefs

Cf. A244869-A244876.

Sequence in context: A116015 A332373 A181945 * A259181 A330088 A281773

Adjacent sequences: A244866 A244867 A244868 * A244870 A244871 A244872

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 08 2014

Status

approved