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 A129092 a(n) = A030067(2^n - 1) for n >= 1, where A030067 is the semi-Fibonacci numbers. 8
 1, 2, 5, 16, 69, 430, 4137, 64436, 1676353, 74555322, 5777029421, 792086153688, 194591768192733, 86534148901444102, 70244955881077121873, 104827174339054175240700, 289320796542222620694103961 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..17. FORMULA Equals the row sums and first column of triangle A129100: a(n) = A129100(n,0), where column 0 of matrix power A129100^(2^k) = column k of A129100 for k > 0. EXAMPLE The semi-Fibonacci sequence (A030067) starts: [(1), 1, (2), 1, 3, 2, (5), 1, 6, 3, 9, 2, 11, 5, (16), 1, ...], and obeys the recurrence: A030067(n) = A030067(n/2) when n is even; and A030067(n) = A030067(n-1) + A030067(n-2) when n is odd. This sequence also equals row sums of triangle A129100: 1; 1, 1; 2, 2, 1; 5, 6, 4, 1; 16, 24, 20, 8, 1; 69, 136, 136, 72, 16, 1; 430, 1162, 1360, 880, 272, 32, 1; ... where columns of A129100 shift left under matrix square, so that A129100^2 starts: 1; 2, 1; 6, 4, 1; 24, 20, 8, 1; 136, 136, 72, 16, 1; 1162, 1360, 880, 272, 32, 1; ... PROG (PARI) /* Generated as column 0 of triangle A129100: */ a(n)=local(A=Mat(1), B); for(m=1, n+1, B=matrix(m, m); for(r=1, m, for(c=1, r, if(r==c || r==1 || r==2, B[r, c]=1, if(c==1, B[r, 1]=sum(i=1, r-1, A[r-1, i]), B[r, c]=(A^(2^(c-1)))[r-c+1, 1])); )); A=B); return(A[n+1, 1]) CROSSREFS Cf. A030067, A129093, A129094. Sequence in context: A059295 A259408 A251684 * A110710 A245881 A078639 Adjacent sequences: A129089 A129090 A129091 * A129093 A129094 A129095 KEYWORD nonn AUTHOR Paul D. Hanna, Mar 29 2007 STATUS approved

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Last modified September 11 21:10 EDT 2024. Contains 375839 sequences. (Running on oeis4.)