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5, 45, 117, 221, 357, 525, 725, 957, 1221, 1517, 1845, 2205, 2597, 3021, 3477, 3965, 4485, 5037, 5621, 6237, 6885, 7565, 8277, 9021, 9797, 10605, 11445, 12317, 13221, 14157, 15125, 16125, 17157, 18221
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Bisection of A078371. - Lambert Klasen (Lambert.Klasen(AT)gmx.net), Nov 19 2004
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FORMULA
| 1 = Sum(0 through infinity): 4/a(n). Sum(k = 0 through n) 4/a(k) = 4(n+1)/[4(n+1)+1] Definite integral(0 to 1) 1/(1 + x^4) = Sum(0 through infinity) 4/a(2n) = Sum(0 through infinity) (-1)^n/(4n+1) - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 18 2003
1 = 1/5 + Sum(n=1, inf, 16/a(n)); with partial sums (4n+1)/(4n+5). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 18 2003
O.g.f.: (-5-30*x+3*x^2)/(-1+x)^3. a(3n)=A001513(2n). Conjecture: a(n+1)-a(n)=A063164(n+2). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 04 2008
a(n)=32*n+a(n-1)+8 (with a(0)=5)[From Vincenzo Librandi (vincenzo.librandi(AT)tin.it)
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EXAMPLE
| For n=1, a(1)=32*1+5+8=45; a(2)=32*2+45+8=117; a(3)=32*3+117+8=221 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it)
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PROG
| (PARI) for(n=0, 80, print1((4*n+3)*(4*n+7), ", "))
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CROSSREFS
| Cf. A078371, A003185.
Sequence in context: A058792 A113948 A096763 * A201876 A027801 A079139
Adjacent sequences: A003182 A003183 A003184 * A003186 A003187 A003188
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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