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A269441
Alternating sum of 10-gonal (or decagonal) pyramidal numbers.
0
0, -1, 10, -28, 62, -113, 188, -288, 420, -585, 790, -1036, 1330, -1673, 2072, -2528, 3048, -3633, 4290, -5020, 5830, -6721, 7700, -8768, 9932, -11193, 12558, -14028, 15610, -17305, 19120, -21056, 23120, -25313, 27642, -30108, 32718, -35473, 38380, -41440, 44660
OFFSET
0,3
LINKS
FORMULA
G.f.: x*(1 - 7*x)/((x - 1)*(x + 1)^4).
a(n) = ((-1)^n*(16*n^3 + 30*n^2 - 4*n - 9) + 9) /24.
a(n) = Sum_{k = 0..n} (-1)^k*A007585(k).
Sum_{n>=1} 1/a(n) = -0.9251958836055717745244669... . - Vaclav Kotesovec, Feb 26 2016
MATHEMATICA
Table[((-1)^n (16 n^3 + 30 n^2 - 4 n - 9) + 9)/24, {n, 0, 40}]
LinearRecurrence[{-3, -2, 2, 3, 1}, {0, -1, 10, -28, 62}, 41]
PROG
(Magma) [((-1)^n*(16*n^3+30*n^2-4*n-9)+9)/24: n in [0..40]]; // Vincenzo Librandi, Feb 27 2016
KEYWORD
easy,sign
AUTHOR
Ilya Gutkovskiy, Feb 26 2016
STATUS
approved