A165999 Triangle read by rows: T(0,0) = 1, T(n,k) = T(n-1,k-1) + T(n-1,k) for n > 0, 0 < k <= trinv(n), where trinv(n) = floor((1+sqrt(1+8*n))/2), and entries outside triangle are 0.

1, 1, 1, 1, 2, 1, 3, 2, 1, 4, 5, 1, 5, 9, 1, 6, 14, 9, 1, 7, 20, 23, 1, 8, 27, 43, 1, 9, 35, 70, 1, 10, 44, 105, 70, 1, 11, 54, 149, 175, 1, 12, 65, 203, 324, 1, 13, 77, 268, 527, 1, 14, 90, 345, 795, 1, 15, 104, 435, 1140, 795, 1, 16, 119, 539, 1575, 1935, 1, 17, 135, 658, 2114

Offset

0,5

Comments

There are trinv(n) terms in row n (see A002024). Related to A136730.

Links

Table of n, a(n) for n=0..71.

Example

Triangle begins: [1] [1, 1] [1, 2] [1, 3, 2] [1, 4, 5] [1, 5, 9] [1, 6, 14, 9] [1, 7, 20, 23] [1, 8, 27, 43] [1, 9, 35, 70] [1, 10, 44, 105, 70] [1, 11, 54, 149, 175] [1, 12, 65, 203, 324] [1, 13, 77, 268, 527] [1, 14, 90, 345, 795] [1, 15, 104, 435, 1140, 795]

Prog

(PARI) trinv(n) = floor((1+sqrt(1+8*n))/2); f(n) = trinv(n-1); s=19; M=matrix(s, s); for(n=1, s, M[n, 1]=1); for(n=2, s, for(k=2, f(n), M[n, k]=M[n-1, k-1]+M[n-1, k])); for(n=1, s, for(k=1, f(n), print1(M[n, k], ", ")))

Crossrefs

A101482 (diagonal T(A000217(n), n))

Sequence in context: A209562 A259344 A239030 * A049280 A108786 A008315

Adjacent sequences: A165996 A165997 A165998 * A166000 A166001 A166002

Keyword

nonn,tabf

Author

Gerald McGarvey, Oct 03 2009

Status

approved