A081663 -id:A081663 - cp's OEIS frontend

A081666 n*3^(n-1)+A081567(n).

1, 4, 16, 62, 233, 855, 3083, 10978, 38746, 135924, 474955, 1655789, 5766389, 20080608, 69976772, 244166410, 853410637, 2988825507, 10490538559, 36905911166, 130139760590, 459970519296, 1629395348591, 5784362027257

Offset: 0

Paul Barry, Mar 26 2003

Binomial transform of A081663.

Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (11,-44,75,-45).

Cf. A000045.

LinearRecurrence[{11,-44,75,-45},{1,4,16,62},30] (* Harvey P. Dale, Aug 06 2022 *)

a(n)=A027471(n-1)+A081567(n) G.f.: (1-7x+16x^2-13x^3)/((3x - 1)^2(5x^2-5x+1))

A125100 Triangle read by rows: T(n,k) = Fibonacci(k+1)binomial(n,k) + (k+1)binomial(n,k+1) (0 <= k <= n).

Original entry on oeis.org

1, 2, 1, 3, 4, 2, 4, 9, 9, 3, 5, 16, 24, 16, 5, 6, 25, 50, 50, 30, 8, 7, 36, 90, 120, 105, 54, 13, 8, 49, 147, 245, 280, 210, 98, 21, 9, 64, 224, 448, 630, 616, 420, 176, 34, 10, 81, 324, 756, 1260, 1512, 1344, 828, 315, 55, 11, 100, 450, 1200, 2310, 3276, 3570, 2880, 1620

Offset: 0

Gary W. Adamson, Nov 20 2006

Binomial transform of the bidiagonal matrix with the Fibonacci numbers (1, 1, 2, 3, 5, 8, ...) in the main diagonal and (1, 2, 3, ...) in the subdiagonal.

Sum of terms in row n = n*2^(n-1) + Fibonacci(2n+1) (A081663).

			First few rows of the triangle:
  1;
  2,   1;
  3,   4,   2;
  4,   9,   9,   3;
  5,  16,  24,  16,   5;
  6,  25,  50,  50,  30,   8;
  7,  36,  90, 120, 105,  54,  13;
  8,  49, 147, 245, 280, 210,  98,  21;
  ...

Cf. A081663, A081659.

Cf. A000045.

with(combinat): T:=(n,k)->binomial(n,k)*fibonacci(k+1)+(k+1)*binomial(n,k+1): for n from 0 to 11 do seq(T(n,k),k=0..n) od; # yields sequence in triangular form

Edited by N. J. A. Sloane, Nov 29 2006

cp's OEIS Frontend

A081666 n*3^(n-1)+A081567(n).

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A125100 Triangle read by rows: T(n,k) = Fibonacci(k+1)binomial(n,k) + (k+1)binomial(n,k+1) (0 <= k <= n).

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cp's OEIS Frontend

A081666 n*3^(n-1)+A081567(n).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

A125100 Triangle read by rows: T(n,k) = Fibonacci(k+1)*binomial(n,k) + (k+1)*binomial(n,k+1) (0 <= k <= n).

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Maple

Extensions

A125100 Triangle read by rows: T(n,k) = Fibonacci(k+1)binomial(n,k) + (k+1)binomial(n,k+1) (0 <= k <= n).