A244874 Number of magic labelings with magic sum n of 6th graph shown in link.

1, 17, 137, 707, 2709, 8417, 22408, 53008, 114251, 228431, 429325, 766167, 1308451, 2151643, 3423880, 5293736, 7979133, 11757477, 16977097, 24070067, 33566489, 46110317, 62476800, 83591624, 110551831, 144648595, 187391933, 240537431, 306115063, 386460183, 484246768

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R. P. Stanley, Examples of Magic Labelings, Unpublished Notes, 1973 [Cached copy, with permission]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 (7,-20,28,-14,-14,28,-20,7,-1).

Formula

G.f.: (1 + 10*x + 38*x^2 + 60*x^3 + 38*x^4 + 10*x^5 + x^6) / ((1 - x)^8*(1 + x)).

a(n) = (-315*(-129+(-1)^n) + 138528*n + 202104*n^2 + 171248*n^3 + 93030*n^4 + 32312*n^5 + 6636*n^6 + 632*n^7) / 40320. - Colin Barker, Jan 11 2017

Mathematica

LinearRecurrence[{7, -20, 28, -14, -14, 28, -20, 7, -1}, {1, 17, 137, 707, 2709, 8417, 22408, 53008, 114251}, 40] (* Harvey P. Dale, Jun 30 2022 *)

Prog

(PARI) Vec((1 + 10*x + 38*x^2 + 60*x^3 + 38*x^4 + 10*x^5 + x^6) / ((1 - x)^8*(1 + x)) + O(x^40)) \\ Colin Barker, Jan 11 2017

Crossrefs

Cf. A244869, A244870, A244871, A244872, A244873, A244875, A244876.

Sequence in context: A041550 A142788 A361150 * A085958 A120784 A357550

Adjacent sequences: A244871 A244872 A244873 * A244875 A244876 A244877

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 08 2014

Status

approved