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A166966 Eigensequence of A047999, Sierpinski's gasket. 4

%I #10 Nov 19 2022 14:50:58

%S 1,2,3,7,8,17,27,66,67,135,204,479,553,1182,1889,4641,4642,9285,13929,

%T 32504,37153,78957,125414,306591,311299,627308,948029,2226203,2570492,

%U 5494707,8782085,21577880,21577881,43155763,64733646,151045177,172623065,366824020,582602867,1424140365

%N Eigensequence of A047999, Sierpinski's gasket.

%C 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).

%F 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, ...).

%o (PARI) T(n, k) = bitand(n-k, k)==0; \\ A047999

%o 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;

%o 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

%Y Cf. A047999, A166967.

%K nonn

%O 0,2

%A _Gary W. Adamson_, Oct 25 2009

%E More terms from _Michel Marcus_, Nov 19 2022

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Last modified May 21 14:18 EDT 2024. Contains 372738 sequences. (Running on oeis4.)