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 A166966 Eigensequence of A047999, Sierpinski's gasket. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified April 18 09:47 EDT 2024. Contains 371779 sequences. (Running on oeis4.)