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 A028557 a(n) = n*(n+5). 22
 0, 6, 14, 24, 36, 50, 66, 84, 104, 126, 150, 176, 204, 234, 266, 300, 336, 374, 414, 456, 500, 546, 594, 644, 696, 750, 806, 864, 924, 986, 1050, 1116, 1184, 1254, 1326, 1400, 1476, 1554, 1634, 1716, 1800, 1886, 1974, 2064, 2156 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(m) where m is a positive integer are the only positive integer values of t for which the Binet-de Moivre formula of the recurrence b(n)=5*b(n-1)+t*b(n-2) with b(0)=0 and b(1)=1 has a root which is a square. In particular sqrt(5^2+4*t) is an integer since 5^2+4*t=5^2+4*a(m)=(2*m+5)^2. Thus the characteristic roots are r1=m+5 and r2=-m. - Felix P. Muga II, Mar 27 2014 LINKS Shawn A. Broyles, Table of n, a(n) for n = 0..1000 P. De Geest, Palindromic Quasipronics of the form n(n+x) F. P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, March 2014; Preprint on ResearchGate. Index entries for linear recurrences with constant coefficients, signature (3,-3,1). FORMULA a(n) = 2*A055998(n). a(n) = 2*n+a(n-1)+4. - Vincenzo Librandi, Aug 05 2010 Sum_{n>=1} 1/a(n) = 137/300 = 0.4566666... - R. J. Mathar, Mar 22 2011 MAPLE with(combinat): seq(fibonacci(3, n)+n-7, n=2..46); # Zerinvary Lajos, Jun 07 2008 with(finance): seq(add(cashflows([2, k, k], 0), k=2..n), n=1..51); # Zerinvary Lajos, Jun 22 2008 MATHEMATICA s=0; lst={s}; Do[s+=n++ +6; AppendTo[lst, s], {n, 0, 6!, 2}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 16 2008 *) Table[n(n+5), {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, May 19 2011 *) PROG (PARI) a(n)=n*(n+5) \\ Charles R Greathouse IV, Jun 17 2017 CROSSREFS Cf. A104675, A002522. Sequence in context: A005281 A120345 A107400 * A104675 A083657 A228435 Adjacent sequences:  A028554 A028555 A028556 * A028558 A028559 A028560 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified September 19 15:00 EDT 2018. Contains 315195 sequences. (Running on oeis4.)