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-1, 2, 7, 14, 23, 34, 47, 62, 79, 98, 119, 142, 167, 194, 223, 254, 287, 322, 359, 398, 439, 482, 527, 574, 623, 674, 727, 782, 839, 898, 959, 1022, 1087, 1154, 1223, 1294, 1367, 1442, 1519, 1598, 1679, 1762, 1847, 1934, 2023, 2114, 2207
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| For n>=2, least m>=1 such that f(m,n)=0 where f(m,n)=sum(i=0,m,sum(k=0,i,(-1)^k*(floor(i/n^k)-n*floor(i/n^(k+1))))) - Benoit Cloitre (benoit7848c(AT)orange.fr), May 02 2004
For n=>3, the a(n)-th row of Pascal's triangle always contains a triple forming an arithmetic progression. - Lekraj Beedassy (blekraj(AT)yahoo.com), Jun 03 2004
Contribution from Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 29 2009: (Start)
Let C = 1 + sqrt(2) = 2.414213...; and 1/C = .414213...
Then a(n) = (n + 1 + 1/C) * (n + 1 - C). Example: a(6) = 34 =
(7 + .414...) * (7 - 2.414...) (End)
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LINKS
| Eric Weisstein's World of Mathematics, Near-Square Prime
Index entries for sequences related to linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| For n>1: a(n) = A143053(A000290(n)), A143054(a(n)) = A000290(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 20 2008
G.f.: (x-5*x^2+2*x^3)/(-1+3*x-3*x^2+x^3). - Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 17 2008
a(n+1) = A101986(n)-A101986(n-1) = A160805(n)-A160805(n-1). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 26 2009
For n>1, a(n) = floor(n^5/(n^3+n+1)). - Gary Detlefs (gdetlefs(AT)aol.com), Feb 10 2010
a(n) = a(n-1)+2*n-1 (with a(1)=-1). - Vincenzo Librandi, Nov 18 2010
Right edge of the triangle in A195437: a(n) = A195437(n-2,n-2). - Reinhard Zumkeller, Nov 23 2011
a(n)*a(n-1)+2 = (a(n)-n)^2 = A028552(n-2)^2. - Bruno Berselli, Dec 07 2011
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MAPLE
| with(combinat, fibonacci):seq(fibonacci(3, i)-3, i=1..47); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 20 2008
a:=n->sum(k-1, k=0..n):seq(a(n)+sum(k, k=2..n), n=1..54); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 10 2008
seq(floor(n^5/(n^3+n+1)), n=2..25); [From Gary Detlefs (gdetlefs(AT)aol.com), Feb 10 2010]
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MATHEMATICA
| s=-1; lst={}; Do[s+=n-3; AppendTo[lst, s], {n, 2, 6!, 2}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 04 2008]
Range[50]^2-2 (* From Harvey P. Dale, Mar 14 2011 *)
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PROG
| sage: [lucas_number1(3, n, 2) for n in xrange(1, 43)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 03 2008
(PARI) {for(n=1, 47, print1(n^2-2, ", "))} [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 17 2008]
(Other) sage: [lucas_number1(3, n, 2) for n in xrange(1, 48)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 16 2009]
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CROSSREFS
| Cf. A145067 (Zero followed by partial sums of A008865). [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Oct 17 2008]
Cf. A000027, A013648 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 11 2009]
Sequence in context: A187142 A161702 A087324 * A018392 A051640 A119354
Adjacent sequences: A008862 A008863 A008864 * A008866 A008867 A008868
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KEYWORD
| sign,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy
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