OFFSET
1,2
COMMENTS
Except for the first term, numbers m such that 36*m^2 + 72*m + 35 = (6*m+5)*(6*m+7) is not of the form p*(p+2), with p prime. - Vincenzo Librandi, Aug 05 2010
Nonnegative k such that k or 4*k + 1 is divisible by 7. - Bruno Berselli, Feb 13 2018
LINKS
David Lovler, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
a(n) = 7*n - a(n-1) - 9 for n>1, with a(1)=0. - Vincenzo Librandi, Aug 05 2010
a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=5 and b(k)=A005009(k-1)=7*2^(k-1) for k>0. - Philippe Deléham, Oct 17 2011
From Bruno Berselli, Oct 17 2011: (Start)
G.f.: x^2*(5 + 2*x)/((1 + x)*(1 - x)^2).
a(n) = (14*n + 3*(-1)^n - 11)/4.
a(-n) = -A047352(n+2). (End)
a(n) = ceiling((7/3)*ceiling(3*n/2)). - Clark Kimberling, Jul 04 2012
E.g.f.: 2 + ((14*x - 11)*exp(x) + 3*exp(-x))/4. - David Lovler, Sep 11 2022
MATHEMATICA
{#, 5 + #} &/@ (7 Range[0, 30]) // Flatten (* or *) LinearRecurrence[{1, 1, -1}, {0, 5, 7}, 60] (* Harvey P. Dale, Dec 01 2016 *)
PROG
(Magma) &cat[[7*n, 7*n+5]: n in [0..23]]; // Bruno Berselli, Oct 17 2011
(PARI) a(n) = (14*n + 3*(-1)^n - 11)/4 \\ David Lovler, Sep 11 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved