A288835 -id:A288835 - cp's OEIS frontend

A288836 a(n) = (1/3!)3^(n+1)(n+5)(n+1)(n).

18, 189, 1296, 7290, 36450, 168399, 734832, 3070548, 12400290, 48715425, 187067232, 704690766, 2611501074, 9542023155, 34437376800, 122941435176, 434685788658, 1523724783237, 5299912289520, 18305618105250, 62824881337218, 214364018189079, 727538485975056

Offset: 1

Gregory Gerard Wojnar, Jun 17 2017

nonn

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (12, -54, 108, -81).

Column k=6 of A287768.

Cf. A288834, A288835, A288838.

LinearRecurrence[{12,-54,108,-81},{18,189,1296,7290},30] (* Harvey P. Dale, May 09 2025 *)

O.g.f.: z*3^2*(2-3*z)/(1-3*z)^4.

a(n) = -A287768(n+5,6).

A288838 a(n) = (1/4!)3^(n+2)(n+7)(n+2)(n+1)*(n).

Original entry on oeis.org

54, 729, 6075, 40095, 229635, 1194102, 5786802, 26572050, 116917020, 496897335, 2051893701, 8269753401, 32643763425, 126557359740, 482984209620, 1817776934388, 6757388169138, 24843338857125, 90429753439935, 326206114635555, 1167092987918319, 4144371018322194

Offset: 1

Gregory Gerard Wojnar, Jun 17 2017

Index entries for linear recurrences with constant coefficients, signature (15,-90,270,-405,243).

Column k=9 of A287768.

Cf. A288834, A288835, A288836.

Table[1/4! 3^(n+2) (n+7)(n+2)(n+1)n,{n,30}] (* or *) LinearRecurrence[{15,-90,270,-405,243},{54,729,6075,40095,229635},30] (* Harvey P. Dale, May 15 2022 *)

a(n)=3^n*3*n*(n+1)*(n+2)*(n+7)/8 \\ Charles R Greathouse IV, Jun 19 2017

O.g.f.: z*3^3*(2-3*z)/(1-3*z)^5.

a(n) = A287768(n+7,9).

A288842 Triangle (sans apex) of coefficients of terms of the form (eM_1)^j*(eM_2)^k re construction of triangle A287768.

Original entry on oeis.org

1, 2, 3, 9, 6, 9, 36, 45, 18, 27, 135, 243, 189, 54, 81, 486, 1134, 1296, 729, 162, 243, 1701, 4860, 7290, 6075, 2673, 486, 729, 5832, 19683, 36450, 40095, 26244, 9477, 1458, 2187, 19683, 76545, 168399, 229635, 199017, 107163, 32805, 4374, 6561, 65610, 288684, 734832, 1194102, 1285956, 918540, 419904, 111537, 13122

Offset: 1

Gregory Gerard Wojnar, Jun 17 2017

			Triangle begins:
  1,  2;
  3,  9,  6;
  9, 36, 45, 18;

G. G. Wojnar, D. Sz. Wojnar, and L. Q. Brin, Universal Peculiar Linear Mean Relationships in All Polynomials, Table GW.n=3, p.22, arXiv:1706.08381 [math.GM], 2017.

Columns are: A000244, A288834, A288835, A288836, A288838, etc.

Cf. A287768.

T[1, 1] = 1; T[1, 2] = 2;
T[n_, k_] /; 1 <= k <= n+1 := T[n, k] = 3 T[n-1, k-1] + 3 T[n-1, k];
T[, ] = 0;
Table[T[n, k], {n, 1, 9}, {k, 1, n+1}] // Flatten (* Jean-François Alcover, Nov 16 2018 *)

T(n+1,k+1) = 3*T(n,k) + 3*T(n,k+1).

cp's OEIS Frontend

A288836 a(n) = (1/3!)3^(n+1)(n+5)(n+1)(n).

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A288838 a(n) = (1/4!)3^(n+2)(n+7)(n+2)(n+1)*(n).

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A288842 Triangle (sans apex) of coefficients of terms of the form (eM_1)^j*(eM_2)^k re construction of triangle A287768.

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cp's OEIS Frontend

A288836 a(n) = (1/3!)*3^(n+1)*(n+5)*(n+1)*(n).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A288838 a(n) = (1/4!)*3^(n+2)*(n+7)*(n+2)*(n+1)*(n).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A288842 Triangle (sans apex) of coefficients of terms of the form (eM_1)^j*(eM_2)^k re construction of triangle A287768.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A288836 a(n) = (1/3!)3^(n+1)(n+5)(n+1)(n).

A288838 a(n) = (1/4!)3^(n+2)(n+7)(n+2)(n+1)*(n).