A244497 Number of magic labelings of the prism graph I X C_5 with magic sum n.

1, 11, 57, 197, 533, 1223, 2494, 4654, 8105, 13355, 21031, 31891, 46837, 66927, 93388, 127628, 171249, 226059, 294085, 377585, 479061, 601271, 747242, 920282, 1123993, 1362283, 1639379, 1959839, 2328565, 2750815, 3232216, 3778776, 4396897, 5093387, 5875473, 6750813, 7727509, 8814119

Offset

0,2

Comments

This sequence is also the number of magic labelings of the cycle-of-loops graph LOOP X C_5 with magic sum n, where LOOP is the 1-vertex, 1-loop-edge graph. A similar identity holds between the sequences for I X C_k and LOOP X C_k for all odd k. - David J. Seal, Sep 14 2017

Links

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

R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]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 + 6*x + 11*x^2 + 6*x^3 + x^4) / ((1 - x)^6*(1 + x)).

From Colin Barker, Jan 13 2017: (Start)

a(n) = (3*(63+(-1)^n) + 576*n + 720*n^2 + 460*n^3 + 150*n^4 + 20*n^5) / 192.

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)

Maple

A244497:=n->(3*(63+(-1)^n) + 576*n + 720*n^2 + 460*n^3 + 150*n^4 + 20*n^5) / 192: seq(A244497(n), n=0..50); # Wesley Ivan Hurt, Sep 16 2017

Mathematica

CoefficientList[Series[(1 + 6 x + 11 x^2 + 6 x^3 + x^4)/((1 - x)^6*(1 + x)), {x, 0, 37}], x] (* Michael De Vlieger, Sep 15 2017 *)
LinearRecurrence[{5, -9, 5, 5, -9, 5, -1}, {1, 11, 57, 197, 533, 1223, 2494}, 40] (* Harvey P. Dale, Aug 04 2021 *)

Prog

(PARI) Vec((1+6*x+11*x^2+6*x^3+x^4) / ((1-x)^6*(1+x)) + O(x^40)) \\ Colin Barker, Jan 13 2017

Crossrefs

Cf. A019298, A061927, A292281, A244873, A289992 (analogues for prism graphs I X C_k, k = 3,4,6,7,8).

Cf. A006325, A244879, A244880 (analogues for LOOP X C_k, k = 4,6,8).

Sequence in context: A071984 A323039 A211614 * A101094 A187693 A200529

Adjacent sequences: A244494 A244495 A244496 * A244498 A244499 A244500

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 07 2014

Status

approved