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

Author

Gary W. Adamson, Oct 25 2009

Keywords

• nonn

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).

Crossrefs

Cf. A047999, A166967.

Programs

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

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, ...).

Extensions

More terms from Michel Marcus, Nov 19 2022