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A125101 T(n,k)=k*binomial(n-1,k-1) + fibonacci(k)*binomial(n-1,k) (1<=k<=n). 0
1, 2, 2, 3, 5, 3, 4, 9, 11, 4, 5, 14, 26, 19, 5, 6, 20, 50, 55, 30, 6, 7, 27, 85, 125, 105, 44, 7, 8, 35, 133, 245, 280, 182, 62, 8, 9, 44, 196, 434, 630, 560, 300, 85, 9, 10, 54, 276, 714, 1260, 1428, 1056, 477, 115, 10, 11, 65, 375, 1110, 2310, 3192, 3030, 1905, 745, 155 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums are s(n) = 1, 4, 11, 28, 69, 167, 400,...

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

LINKS

Table of n, a(n) for n=1..65.

FORMULA

T(n,2) = A000096(n-1).

T(n,3) = A051925(n-1).

T(n,4) = A215862(n-3). - R. J. Mathar, Aug 10 2013

Row sums s(n) = 7*s(n-1) -17*s(n-2) +16*s(n-3) -4*s(n-4) with s(n) = A001787(n+1)/4 +A001906(n-1). - R. J. Mathar, Aug 10 2013

EXAMPLE

First few rows of the triangle are:

1;

2, 2;

3, 5, 3;

4, 9, 11, 4;

5, 14, 26, 19, 5;

6, 20, 50, 55, 30, 6;

7, 27, 85, 125, 105, 44, 7;

8, 35, 133, 245, 280, 182, 62, 8;

...

MAPLE

with(combinat): T:=(n, k)->k*binomial(n-1, k-1)+fibonacci(k)*binomial(n-1, k): for n from 1 to 12 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form

MATHEMATICA

Flatten[Table[k Binomial[n-1, k-1]+Fibonacci[k]Binomial[n-1, k], {n, 15}, {k, n}]] (* Harvey P. Dale, Nov 03 2014 *)

CROSSREFS

Cf. A000096, A051925.

Sequence in context: A196957 A124727 A210565 * A208519 A210232 A047666

Adjacent sequences:  A125098 A125099 A125100 * A125102 A125103 A125104

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Nov 20 2006

EXTENSIONS

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

STATUS

approved

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Last modified November 16 17:04 EST 2019. Contains 329201 sequences. (Running on oeis4.)