A195661 Number of ways to place 12n nonattacking kings on a vertical cylinder 24 X 2n.

8192, 1270246, 44653028, 720390254, 7177627944, 51526819510, 291859775552, 1382652697282, 5700499630916, 21042965606234, 71028444904044, 222770819826574, 657397551407816, 1843639061043694, 4953451546255928, 12835026767559890, 32249277650536068

Offset

1,1

Comments

Vertical cylinder: a chessboard where it is supposed that the columns 1 and 24 are in contact (number of columns = 24, number of rows = 2n).

Links

Table of n, a(n) for n=1..17.

V. Kotesovec, Non-attacking chess pieces

Index entries for linear recurrences with constant coefficients, signature (15, -103, 429, -1210, 2442, -3630, 4026, -3333, 2035, -891, 265, -48, 4).

Formula

Recurrence: a(n) = 4*a(n-13) - 48*a(n-12) + 265*a(n-11) - 891*a(n-10) + 2035*a(n-9) - 3333*a(n-8) + 4026*a(n-7) - 3630*a(n-6) + 2442*a(n-5) - 1210*a(n-4) + 429*a(n-3) - 103*a(n-2) + 15*a(n-1).

G.f.: -(1 + 8177*x + 1147469*x^2 + 26442685*x^3 + 177917014*x^4 + 436010362*x^5 + 423443926*x^6 + 163698250*x^7 + 23613841*x^8 + 1078869*x^9 + 9965*x^10 + 41*x^11)/((x-1)^11*(2*x-1)^2).

a(n) = (74405871551*n - 1097352668753)*2^n + 696317/2016*n^10 + 420699809/30240*n^9 + 66463031/210*n^8 + 26602370087/5040*n^7 + 33515235289/480*n^6 + 1076425504013/1440*n^5 + 32380230257101/5040*n^4 + 325331895133417/7560*n^3 + 29685456992323/140*n^2 + 72053208873316/105*n + 1097352668754.

Prog

(PARI) a(n)=((2250033555702240*n-33183944703090720)*2^n+10444755*n^10+420699809*n^9+9570676464*n^8+159614220522*n^7+2111459823207*n^6+22604935584273*n^5+194281381542606*n^4+1301327580533668*n^3+6412058710341768*n^2+20751324155515010*n)/30240+1097352668754 \\ Charles R Greathouse IV, May 30 2026

Crossrefs

Cf. A195656, A195651, A137432.

Sequence in context: A069274 A220585 A305756 * A017690 A010801 A138031

Adjacent sequences: A195658 A195659 A195660 * A195662 A195663 A195664

Keyword

nonn,easy

Author

Vaclav Kotesovec, Sep 22 2011

Status

approved