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A132925
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a(n) = 2^n - 1 + n*(n-1)/2.
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5
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1, 4, 10, 21, 41, 78, 148, 283, 547, 1068, 2102, 4161, 8269, 16474, 32872, 65655, 131207, 262296, 524458, 1048765, 2097361, 4194534, 8388860, 16777491, 33554731, 67109188, 134218078, 268435833, 536871317, 1073742258, 2147484112
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OFFSET
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1,2
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COMMENTS
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Row sums of triangle A132924. n-th Mersenne number + (n-1)-th triangular number.
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LINKS
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FORMULA
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Binomial transform of [1, 3, 3, 2, 2, 2, 2, ...].
a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4); a(1)=1, a(2)=4, a(3)=10, a(4)=21. - Harvey P. Dale, Jun 19 2011
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EXAMPLE
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a(4) = 21 = sum of row 4 terms of triangle A132924: (4 + 4 + 5 + 8).
a(4) = 21 = (1, 3, 3, 1) dot (1, 3, 3, 2) = (1 + 9 + 9 + 2).
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MAPLE
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MATHEMATICA
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Table[2^n-1+n (n-1)/2, {n, 40}] (* or *) LinearRecurrence[{5, -9, 7, -2}, {1, 4, 10, 21}, 40] (* Harvey P. Dale, Jun 19 2011 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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