A166966 Eigensequence of A047999, Sierpinski's gasket.

1, 2, 3, 7, 8, 17, 27, 66, 67, 135, 204, 479, 553, 1182, 1889, 4641, 4642, 9285, 13929, 32504, 37153, 78957, 125414, 306591, 311299, 627308, 948029, 2226203, 2570492, 5494707, 8782085, 21577880, 21577881, 43155763, 64733646, 151045177, 172623065, 366824020, 582602867, 1424140365

Offset

0,2

Comments

Equals row sums of triangle A166967. Prefaced with a 1: (1, 1, 2, 3, 7, 8, 17, ...) has an apparent parity of (1, 1, 0, ... repeat).

Links

Table of n, a(n) for n=0..39.

Formula

Eigensequence of triangle A047999. Let triangle Q = a one-row-shifted-down version of Sierpinski's gasket, placing a "1" at top. Take lim_{n->oo} Q^n, resulting in a one-column vector [1, 1, 2, 3, 7, ...]. Then delete the first "1", getting A166966: (1, 2, 3, 7, 8, 17, ...).

Prog

(PARI) T(n, k) = bitand(n-k, k)==0; \\ A047999
shiftm(m, nn) = my(shm=matrix(nn+1, nn+1)); shm[1, 1]=1; for (n=1, nn, for(k=1, nn, shm[n+1, k] = m[n, k]; ); ); shm;
lista(nn) = my(m=matrix(nn, nn, n, k, T(n-1, k-1)), shm=shiftm(m, nn), shmnn=shm^nn); vector(nn, k, shmnn[k+1, 1]); \\ Michel Marcus, Nov 19 2022

Crossrefs

Cf. A047999, A166967.

Sequence in context: A244508 A060121 A002964 * A247843 A181658 A251541

Adjacent sequences: A166963 A166964 A166965 * A166967 A166968 A166969

Keyword

nonn

Author

Gary W. Adamson, Oct 25 2009

Extensions

More terms from Michel Marcus, Nov 19 2022

Status

approved