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 A244497 Number of magic labelings of the prism graph I X C_5 with magic sum n. 13
 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 (list; graph; refs; listen; history; text; internal format)
 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J. Seal, Sep 14 2017 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission] Index entries for linear recurrences with constant coefficients, signature (5,-9,5,5,-9,5,-1).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

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Last modified June 9 23:59 EDT 2023. Contains 363183 sequences. (Running on oeis4.)