A139821 Triangle T(i,j) read by rows: T(i,1) = Fibonacci(i) for all i; T(i,i) = i for all i; T(i,j) = T(i-1,j) + T(i-2,j) + T(i-1,j-1) - T(i-2,j-1).

1, 1, 2, 2, 2, 3, 3, 5, 3, 4, 5, 8, 9, 4, 5, 8, 15, 15, 14, 5, 6, 13, 26, 31, 24, 20, 6, 7, 21, 46, 57, 54, 35, 27, 7, 8, 34, 80, 108, 104, 85, 48, 35, 8, 9, 55, 139, 199, 209, 170, 125, 63, 44, 9, 10, 89, 240, 366, 404, 360, 258, 175, 80, 54, 10, 11

Offset

1,3

Comments

Sum of n-th row terms = (2^n - 1) (see solution in Fibonacci Quarterly).

Links

Table of n, a(n) for n=1..66.

Jyoti P. Shiwalker and M. N. Despande, Problem B-1033, Fibonacci Quarterly, Vol. 45, Number 2; 2007; p. 181.

Russ Euler and Jawad Sadek, editors, Elementary Problems and Solutions, Fibonacci Quarterly, Vol. 45, Number 4; 2007; p. 181.

Example

First few rows of the triangle are:
1;
1, 2;
2, 2, 3;
3, 5, 3, 4;
5, 8, 9, 4, 5;
8, 15, 15, 14, 5, 6;
13, 26, 31, 24, 20, 6, 7;
21, 46, 57, 54, 5, 27, 7, 8;
...

Prog

(PARI) t(i, j) = {if ((i <= 0) || (j <= 0), 0, if (j == 1, fibonacci(i), if (i == j, i, t(i-1, j) + t(i-2, j) + t(i-1, j-1) - t(i-2, j-1); ); ); ); }
tabl(nn) = {for (n=1, nn, for (k=1, n, print1(t(n, k), ", "); ); ); } \\ Michel Marcus, Feb 11 2014

Crossrefs

Sequence in context: A293440 A237121 A329493 * A248972 A077563 A055256

Adjacent sequences: A139818 A139819 A139820 * A139822 A139823 A139824

Keyword

nonn,tabl

Author

Gary W. Adamson, May 01 2008

Extensions

More terms from Michel Marcus, Feb 11 2014

Status

approved