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A181475
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a(n) = 3*n^4 + 6*n^3 - 3*n + 1.
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2
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1, 7, 91, 397, 1141, 2611, 5167, 9241, 15337, 24031, 35971, 51877, 72541, 98827, 131671, 172081, 221137, 279991, 349867, 432061, 527941, 638947, 766591, 912457, 1078201, 1265551, 1476307, 1712341, 1975597, 2268091, 2591911, 2949217, 3342241, 3773287, 4244731
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OFFSET
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0,2
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COMMENTS
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If gcd(n,7)=gcd(n+1,7)=gcd(2*n+1,7)=1 then a(n)==0 (mod 7) (E. Picutti, see References).
Last digit: (17*(n mod 5)+77*(n+1 mod 5)-43*(n+2 mod 5)+77*(n+3 mod 5)-43*(n+4 mod 5))/50 (cf. forms of modular arithmetic of Paolo P. Lava, i.e. see A146094).
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REFERENCES
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Ettore Picutti, Sul numero e la sua storia, Feltrinelli Economica, 1977, p. 208.
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LINKS
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B. Berselli, Table of n, a(n) for n = 0..10000.
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
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FORMULA
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G.f.: (1+2*x+66*x^2+2*x^3+x^4)/(1-x)^5.
a(n) = a(-n-1) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5).
a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4)+6*12.
a(n) = 3*a(n-1)-3*a(n-2)+a(n-3)+ 6*A008594(n-1).
a(n) = 2*a(n-1)-a(n-2)+6*A003154(n).
a(n) = a(n-1)+6*A007588(n).
a(n) = 1+6*A062392(n).
a(n) = 7*A000540(n)/A000330(n) = A154105(A000096(n-1)) for n>0.
Sum(a(i), i=0..n) = (3*n^5+15*n^4+20*n^3-3*n+5)/5.
a(n) = 7*(3*n^2+3*n-1)*sum(k^6, k=1..n)/(5*sum(k^4, k=1..n)), n>0. - Gary Detlefs, Oct 18 2011
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MATHEMATICA
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Table[3 n^4 + 6 n^3 - 3 n + 1, {n, 0, 40}] (* Vincenzo Librandi, Mar 26 2013 *)
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PROG
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(MAGMA) [3*n^4+6*n^3-3*n+1: n in [0..31]];
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CROSSREFS
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Subsequence of A003215.
Sequence in context: A319978 A085026 A221132 * A249640 A248226 A165230
Adjacent sequences: A181472 A181473 A181474 * A181476 A181477 A181478
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KEYWORD
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nonn,easy
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AUTHOR
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Bruno Berselli, Oct 25 2010 - Oct 29 2010
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EXTENSIONS
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Formula, program and crossref added by Bruno Berselli, Aug 22 2011
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STATUS
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approved
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