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 A114214 Diagonal sums of number triangle A114213. 2
 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 5, 5, 4, 4, 5, 5, 7, 7, 8, 8, 7, 7, 7, 7, 8, 8, 7, 7, 5, 5, 6, 6, 9, 9, 11, 11, 10, 10, 11, 11, 13, 13, 12, 12, 9, 9, 9, 9, 12, 12, 13, 13, 11, 11, 10, 10, 11, 11, 9, 9, 6, 6, 7, 7, 11, 11, 14, 14, 13, 13, 15, 15, 18, 18, 17, 17, 13, 13, 14, 14, 19, 19, 21 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Conjecture: a(n) = A007306(floor(n/2)+1). - Georg Fischer, Nov 28 2022 LINKS Georg Fischer, Table of n, a(n) for n = 0..1000 Jeffrey Shallit and Lukas Spiegelhofer, Continuants, run lengths, and Barry's modified Pascal triangle, arXiv:1710.06203 [math.CO], 2017. FORMULA a(n) = Sum_{k=0..floor(n/2)} mod(Sum_{j=0..n-2k} C(k, j) C(n-2k, j) (1+(-1)^j)/2, 2). (corrected by Jeffrey Shallit, May 18 2016) PROG (PARI) a(n) = sum(k=0, n\2, sum(j=0, n-2*k, binomial(k, j)*binomial(n-2*k, j)*(1+(-1)^j)/2) % 2); \\ Michel Marcus, Jun 06 2021 CROSSREFS Cf. A007306, A114213. Sequence in context: A093875 A329242 A266193 * A321318 A270362 A196383 Adjacent sequences: A114211 A114212 A114213 * A114215 A114216 A114217 KEYWORD easy,nonn AUTHOR Paul Barry, Nov 17 2005 STATUS approved

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