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 A084263 Modified triangular numbers. 4
 1, 1, 4, 6, 11, 15, 22, 28, 37, 45, 56, 66, 79, 91, 106, 120, 137, 153, 172, 190, 211, 231, 254, 276, 301, 325, 352, 378, 407, 435, 466, 496, 529, 561, 596, 630, 667, 703, 742, 780, 821, 861, 904, 946, 991, 1035, 1082, 1128, 1177, 1225, 1276, 1326, 1379, 1431 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n)=A000217(n)+A059841(n). Partial sums are A084570. Binomial transform is A084264. Contribution from Gary W. Adamson, May 14 2010: (Start) Starting with offset 1 = row sums of an infinite lower triangular triangular matrix with alternate columns of (1, 3, 5, 7,...) and (1, 0, 0, 0,...). (End) LINKS FORMULA E.g.f.: cosh(x)+exp(x)(x+x^2/2); a(n)=(-1)^n/2+(n^2+n+1)/2; a(n)=sum{k=0..n, k+(-1)^k}. O.g.f.: -(-x+1+2*x^2)/[(-1+x)^3*(x+1)]. - R. J. Mathar, Apr 02 2008 EXAMPLE Contribution from Gary W. Adamson, May 14 2010: (Start) First few rows of the triangle with row sums = A084263 = 1; 3, 1; 5, 0, 1; 7, 0, 3, 1; 9, 0, 5, 0, 1; 11, 0, 7, 0, 3, 1; ... Example: a(4) = 11 = (7 + 0 + 3 + 1). (End) CROSSREFS Sequence in context: A002732 A144065 A036831 * A060180 A190499 A190564 Adjacent sequences:  A084260 A084261 A084262 * A084264 A084265 A084266 KEYWORD easy,nonn AUTHOR Paul Barry, May 31 2003 STATUS approved

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Last modified May 19 06:05 EDT 2013. Contains 225428 sequences.