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A015226
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Even hexagonal pyramidal numbers.
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2
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22, 50, 252, 372, 946, 1222, 2360, 2856, 4750, 5530, 8372, 9500, 13482, 15022, 20336, 22352, 29190, 31746, 40300, 43460, 53922, 57750, 70312, 74872, 89726, 95082, 112420, 118636, 138650, 145790, 168672, 176800, 202742, 211922, 241116
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OFFSET
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0,1
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LINKS
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FORMULA
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Even numbers of form n(n+1)(4n-1)/6.
Contribution from Ant King, Oct 25 2012: (Start)
a(n) = a(n-1) +3*a(n-2) -3*a(n-3) -3*a(n-4) +3*a(n-5) +a(n-6) -a(n-7).
a(n) = 3*a(n-2) -3*a(n-4) +a(n-6) +256.
a(n) = (4*n+(-1)^n+5)*(4*n+(-1)^n+7)*(8*n+2*(-1)^n+9)/24.
G. f. 2*x*(11 + 14*x + 68*x^2 + 18*x^3 + 17*x^4) / ((1-x)^4*(1+x)^3).
(End)
E.g.f.: (1/6)*(3*(15 - 30*x + 8*x^2)*exp(-x) + (87 + 348*x + 228*x^2 + 32*x^3 ) *exp(x)). - G. C. Greubel, Jul 30 2016
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MATHEMATICA
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Select[ Table[ n(n+1)(4n-1)/6, {n, 100} ], EvenQ ]
LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {22, 50, 252, 372, 946, 1222, 2360}, 35] (* Ant King, Oct 25 2012 *)
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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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EXTENSIONS
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STATUS
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approved
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