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 A114212 Generalized Gould sequence. 1
 1, 2, 3, 4, 4, 4, 6, 8, 6, 4, 6, 8, 8, 8, 12, 16, 10, 4, 6, 8, 8, 8, 12, 16, 12, 8, 12, 16, 16, 16, 24, 32, 18, 4, 6, 8, 8, 8, 12, 16, 12, 8, 12, 16, 16, 16, 24, 32, 20, 8, 12, 16, 16, 16, 24, 32, 24, 16, 24, 32, 32, 32, 48, 64, 34, 4, 6, 8, 8, 8, 12, 16, 12, 8, 12, 16, 16, 16, 24, 32, 20, 8 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row sums of A114213. LINKS Jeffrey Shallit, Lukas Spiegelhofer, Continuants, run lengths, and Barry's modified Pascal triangle, arXiv:1710.06203 [math.CO], 2017. FORMULA a(n) = Sum_{k=0..n} (Sum_{j=0..n-k} C(k, j)*C(n-k, j)*(1 + (-1)^k)/2 mod 2); a(n) = A001316(n) + A001316((n-2)/2)*(1 + (-1)^n)/2. EXAMPLE From Omar E. Pol, Jun 09 2009: (Start) Triangle begins: 1; 2,3; 4,4,4,6; 8,6,4,6,8,8,8,12; 16,10,4,6,8,8,8,12,16,12,8,12,16,16,16,24; 32,18,4,6,8,8,8,12,16,12,8,12,16,16,16,24,32,20,8,12,16,16,16,24,32,24,... Also, we can write the initial term followed by a triangle: 1; 2; 3,4; 4,4,6,8; 6,4,6,8,8,8,12,16; 10,4,6,8,8,8,12,16,12,8,12,16,16,16,24,32; 18,4,6,8,8,8,12,16,12,8,12,16,16,16,24,32,20,8,12,16,16,16,24,32,24,16,... Also, we can write first two terms followed by a triangle: 1; 2; 3; 4,4; 4,6,8,6; 4,6,8,8,8,12,16,10; 4,6,8,8,8,12,16,12,8,12,16,16,16,24,32,18; 4,6,8,8,8,12,16,12,8,12,16,16,16,24,32,20,8,12,16,16,16,24,32,24,16,24,32,... (End) CROSSREFS Cf. A000079. [Omar E. Pol, Jun 09 2009] Sequence in context: A221917 A131798 A206925 * A108355 A057951 A076410 Adjacent sequences:  A114209 A114210 A114211 * A114213 A114214 A114215 KEYWORD easy,nonn AUTHOR Paul Barry, Nov 17 2005 STATUS approved

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Last modified October 23 14:22 EDT 2019. Contains 328345 sequences. (Running on oeis4.)