A259364 -id:A259364 - cp's OEIS frontend

A259395 a(n) = -3n^2(n-1)^4(n+1)(11n^3+49n^2-439*n+171).

0, 0, 15228, 705024, 1885680, -66355200, -792382500, -4986842112, -22516232256, -81696522240, -252908835300, -693126720000, -1723987588752, -3961019252736, -8517765880260, -17315965900800, -33541737120000, -62298041352192, -111515651966916, -193198552634880

Offset: 0

Vincenzo Librandi, Jun 26 2015

M. P. Delest, Generating functions for column-convex polyominoes, J. Combin. Theory Ser. A 48 (1988), no. 1, pp. 12-31. See expression D in Theorem 16 page 29.
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Cf. A001105, A005435, A259364.

[-3*n^2*(n-1)^4*(n+1)*(11*n^3+49*n^2-439*n+171): n in [0..20]];

A259395:=n->-3*n^2*(n-1)^4*(n+1)*(11*n^3+49*n^2-439*n+171): seq(A259395(n), n=0..25); # Wesley Ivan Hurt, Jun 29 2015

Table[-3 n^2 (n - 1)^4 (n + 1) (11 n^3 + 49 n^2 - 439 n + 171), {n, 0, 23}]
LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{0,0,15228,705024,1885680,-66355200,-792382500,-4986842112,-22516232256,-81696522240,-252908835300},20] (* Harvey P. Dale, Jul 07 2025 *)

G.f.: 324*x^2*(47+1659*x - 15531*x^2 - 156895*x^3 - 216255*x^4 - 17547*x^5 + 31451*x^6 + 3471*x^7) / (1-x)^11.

a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11).

A259435 a(n) = 2(n-1)^6(n+1)^2(n^2+10n+1).

Original entry on oeis.org

2, 0, 450, 81920, 2077650, 22413312, 148531250, 716636160, 2763575010, 9017753600, 25850353122, 66816000000, 158678718770, 351151718400, 731985584850, 1449526034432, 2745436781250, 5000952545280, 8800799033090, 15019798118400, 24938174692242, 40392704000000

Offset: 0

Vincenzo Librandi, Jun 27 2015

This appears as the function alpha(n) in Delest, related to bar/bat theory; see section 3.

M. P. Delest, Generating functions for column-convex polyominoes, J. Combin. Theory Ser. A 48 (1988), no. 1, pp. 12-31. See expression E in Theorem 16 page 29.
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).

Cf. A001105, A005435, A259364, A259395.

[2*(n-1)^6*(n+1)^2*(n^2+10*n+1): n in [0..30]];

A259435:=n->2*(n-1)^6*(n+1)^2*(n^2+10*n+1): seq(A259435(n), n=0..30); # Wesley Ivan Hurt, Jun 29 2015

Table[2 (n - 1)^6 (n + 1)^2 (n^2 + 10 n + 1), {n, 0, 30}]
LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{2,0,450,81920,2077650,22413312,148531250,716636160,2763575010,9017753600,25850353122},30] (* Harvey P. Dale, Dec 29 2024 *)

a(n)=2*(n-1)^6*(n+1)^2*(n^2+10*n+1) \\ Charles R Greathouse IV, Jun 29 2015

[2*(n-1)^6*(n+1)^2*(n^2+10*n+1) for n in (0..30)] # Bruno Berselli, Jun 30 2015

G.f.: 2*(1 -11*x + 280*x^2 + 38320*x^3 + 600970*x^4 + 1994794*x^5 + 1444096*x^6 - 231320*x^7 - 207395*x^8 - 10935*x^9)/(1-x)^11.

a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11).

A259563 a(n) = 81n^3(n-1)^5(n+1)^2(n^2-6n+1)(n^3-79n^2+163n-81).

Original entry on oeis.org

0, 0, 2571912, 2472394752, 138662798400, 1666179072000, -4637478825000, -272992368918528, -3187483870330368, -23209723979366400, -126970182577359000, -566493158246400000, -2161675076294530368, -7278963158259007488, -22112928086617859400, -61611251010011136000

Offset: 0

Vincenzo Librandi, Jun 30 2015

M. P. Delest, Generating functions for column-convex polyominoes, J. Combin. Theory Ser. A 48 (1988), no. 1, pp. 12-31. See expression F in Theorem 16 page 29.
Index entries for linear recurrences with constant coefficients, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).

Cf. A001105, A005435, A259364, A259395, A259435.

[81*n^3*(n-1)^5*(n+1)^2*(n^2-6*n+1)*(n^3-79*n^2+163*n-81): n in [0..20]];

Table[81 n^3 (n-1)^5 (n+1)^2 (n^2 - 6 n + 1) (n^3 - 79 n^2 + 163 n - 81), {n, 0, 23}]
LinearRecurrence[{16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1},{0,0,2571912,2472394752,138662798400,1666179072000,-4637478825000,-272992368918528,-3187483870330368,-23209723979366400,-126970182577359000,-566493158246400000,-2161675076294530368,-7278963158259007488,-22112928086617859400,-61611251010011136000},20] (* Harvey P. Dale, Sep 02 2024 *)

G.f.: 52488*x^2*(49 + 46320*x + 1894016*x^2 - 4899760*x^3 - 305530185*x^4 - 1372006208*x^5 - 1287460720*x^6 + 1418574528*x^7 + 2422309735*x^8 + 1000206160*x^9 + 139190784*x^10 + 5654000*x^11 + 37281*x^12)/(1-x)^16.

a(n) = 16*a(n-1) - 120*a(n-2) + 560*a(n-3) - 1820*a(n-4) + 4368*a(n-5) - 8008*a(n-6) + 11440*a(n-7) - 12870*a(n-8) + 11440*a(n-9) - 8008*a(n-10) + 4368*a(n-11) - 1820*a(n-12) + 560*a(n-13) - 120*a(n-14) + 16*a(n-15) - a(n-16).

cp's OEIS Frontend

A259395 a(n) = -3n^2(n-1)^4(n+1)(11n^3+49n^2-439*n+171).

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A259435 a(n) = 2(n-1)^6(n+1)^2(n^2+10n+1).

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A259563 a(n) = 81n^3(n-1)^5(n+1)^2(n^2-6n+1)(n^3-79n^2+163n-81).

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cp's OEIS Frontend

A259395 a(n) = -3*n^2*(n-1)^4*(n+1)*(11*n^3+49*n^2-439*n+171).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Maple

Mathematica

Formula

A259435 a(n) = 2*(n-1)^6*(n+1)^2*(n^2+10*n+1).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Sage

Formula

A259563 a(n) = 81*n^3*(n-1)^5*(n+1)^2*(n^2-6*n+1)*(n^3-79*n^2+163*n-81).

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

Formula

A259395 a(n) = -3n^2(n-1)^4(n+1)(11n^3+49n^2-439*n+171).

A259435 a(n) = 2(n-1)^6(n+1)^2(n^2+10n+1).

A259563 a(n) = 81n^3(n-1)^5(n+1)^2(n^2-6n+1)(n^3-79n^2+163n-81).