OFFSET
1,2
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).
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
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 *)
PROG
(PARI) a(n)=7*n*(n+1)/2-6 \\ Charles R Greathouse IV, Jan 11 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Oct 08 2009
EXTENSIONS
a(35) corrected by Harvey P. Dale, Nov 01 2011
STATUS
approved