A098603 -id:A098603 - cp's OEIS frontend

A132773 a(n) = n*(n + 31).

0, 32, 66, 102, 140, 180, 222, 266, 312, 360, 410, 462, 516, 572, 630, 690, 752, 816, 882, 950, 1020, 1092, 1166, 1242, 1320, 1400, 1482, 1566, 1652, 1740, 1830, 1922, 2016, 2112, 2210, 2310, 2412, 2516, 2622, 2730, 2840, 2952, 3066, 3182, 3300, 3420, 3542, 3666

Offset: 0

Omar E. Pol, Aug 28 2007

Felix P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, Preprint on ResearchGate, March 2014.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A001008, A002378, A005563, A028347, A028552, A028557, A028560, A028563, A028566, A028569.
Cf. A098603, A098847, A098848, A098849, A098850, A102928, A120071, A132758, A132759, A132760.
Cf. A132761, A132762, A132763, A132764, A132765, A132766, A132767, A132768, A132769, A132770.
Cf. A132771, A132772.

Table[n*(n + 31), {n, 0, 100}] (* Wesley Ivan Hurt, Apr 16 2024 *)

a(n)=n*(n+31) \\ Charles R Greathouse IV, Jun 17 2017

G.f.: 2*x*(-16+15*x)/(-1+x)^3. - R. J. Mathar, Nov 14 2007
a(n) = 2*A132758(n). - R. J. Mathar, Jul 22 2009
a(n) = 2*n + a(n-1) + 30, with n > 0, a(0)=0. - Vincenzo Librandi, Aug 03 2010
From Amiram Eldar, Jan 16 2021: (Start)
Sum_{n>=1} 1/a(n) = H(31)/31 = A001008(31)/A102928(31) = 290774257297357/2238255069850800, where H(k) is the k-th harmonic number.
Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/31 - 7313175618421/319750724264400. (End)
From Elmo R. Oliveira, Dec 13 2024: (Start)
E.g.f.: exp(x)*x*(32 + x).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)

A349487 a(n) = A132739((n-5)*(n+5)).

Original entry on oeis.org

11, 24, 39, 56, 3, 96, 119, 144, 171, 8, 231, 264, 299, 336, 3, 416, 459, 504, 551, 24, 651, 704, 759, 816, 7, 936, 999, 1064, 1131, 48, 1271, 1344, 1419, 1496, 63, 1656, 1739, 1824, 1911, 16, 2091, 2184, 2279, 2376, 99, 2576, 2679, 2784, 2891, 24, 3111

Offset: 6

Simon Strandgaard, Nov 19 2021

nonn

Shares 614 initial terms with A061043. First difference is A061043(620)=615 vs. a(620)=123.

			a(9)  = A132739(( 9-5)*( 9+5)) = A132739(56) = 56,
a(10) = A132739((10-5)*(10+5)) = A132739(75) = 3,
a(11) = A132739((11-5)*(11+5)) = A132739(96) = 96.

Cf. A061043, A098603, A132739.

Table[Last@Select[Divisors[(n - 5)*(n + 5)], Mod[#, 5] != 0 &], {n, 6,
   56}] (* Giorgos Kalogeropoulos, Nov 19 2021 *)
Table[(n - 5)*(n + 5)/5^IntegerExponent[(n - 5)*(n + 5), 5], {n, 6, 56}] (* Amiram Eldar, Nov 22 2021 *)

A132739(n)=n/5^valuation(n, 5);
a(n) = A132739((n-5)*(n+5));
[a(n)|n<-[6..25]]

def A349487(n):
    a, b = divmod(n*n-25, 5)
    while b == 0:
        a, b = divmod(a,5)
    return 5*a+b # Chai Wah Wu, Dec 05 2021

p (6..25).map { |n| x = (n-5)*(n+5); x /= 5 while (x % 5) == 0; x }

a(n) = A132739(A098603(n-5)).

cp's OEIS Frontend

A132773 a(n) = n*(n + 31).

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A349487 a(n) = A132739((n-5)*(n+5)).

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