A166146 a(n) = (7*n^2 + 7*n - 12)/2.

1, 15, 36, 64, 99, 141, 190, 246, 309, 379, 456, 540, 631, 729, 834, 946, 1065, 1191, 1324, 1464, 1611, 1765, 1926, 2094, 2269, 2451, 2640, 2836, 3039, 3249, 3466, 3690, 3921, 4159, 4404, 4656, 4915, 5181, 5454, 5734, 6021, 6315, 6616, 6924, 7239, 7561

Offset: 1

Author

Vincenzo Librandi, Oct 08 2009

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000217.

Programs

Mathematica

RecurrenceTable[{a[1]==1,a[n]==a[n-1]+7n},a,{n,50}] (* or *) LinearRecurrence[{3,-3,1},{1,15,36},50] (* Harvey P. Dale, Nov 01 2011 *)
Table[(7 n^2 + 7 n - 12)/2, {n, 46}] (* Michael De Vlieger, Apr 27 2016 *)

PARI

a(n)=7*n*(n+1)/2-6 \\ Charles R Greathouse IV, Jan 11 2012

Formula

a(n) = a(n-1) + 7n, a(1)=1.

From Harvey P. Dale, Nov 01 2011: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(1)=1, a(2)=15, a(3)=36.

G.f.: x*(1+12*x-6*x^2)/(1-x)^3. (End)

E.g.f.: (1/2)*((-12 + 14*x + 7*x^2)*exp(x) + 12). - G. C. Greubel, Apr 26 2016

Sum_{n>=1} 1/a(n) = 1/6 + (2*Pi/sqrt(385))*tan(sqrt(55/7)*Pi/2). - Amiram Eldar, Feb 20 2023

a(n) = T(n) + 12*T(n-1) - 6*T(n-2), where T(n) = A000217(n) is the n-th triangular number. - Gary W. Adamson, Mar 12 2024

Extensions

a(35) corrected by Harvey P. Dale, Nov 01 2011