login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A129111 Sums of three consecutive heptagonal numbers. 1
8, 26, 59, 107, 170, 248, 341, 449, 572, 710, 863, 1031, 1214, 1412, 1625, 1853, 2096, 2354, 2627, 2915, 3218, 3536, 3869, 4217, 4580, 4958, 5351, 5759, 6182, 6620, 7073, 7541, 8024, 8522, 9035, 9563, 10106, 10664, 11237, 11825, 12428, 13046, 13679 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Arises in heptagonal number analog to A129803 (Triangular numbers which are the sum of three consecutive triangular numbers).

What are the heptagonal numbers which are the sum of three consecutive heptagonal numbers?

Prime for a(2) = 59, a(3) = 107, a(7) = 449, a(10) = 863, a(11) = 1031, a(23) = 4217, a(26) = 5351, a(31) = 7541, a(42) = 13679, a(43) = 14327, a(46) = 16361, a(51) = 20051.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).

FORMULA

a(n) = Hep(n) + Hep(n+1) + Hep(n+2) where Hep(n) = A000566(n) = n(5n-3)/2.

a(n) = (15/2)*n^2 + (21/2)*n + 8.

G.f. (8+2*x+5*x^2)/(1-x)^3; a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). - Colin Barker, Feb 20 2012

EXAMPLE

a(0) = Hep(0) + Hep(1) + Hep(2) = 0 + 1 + 7 = 8 = (15/2)*0^2 + (21/2)*0 + 8.

a(1) = Hep(1) + Hep(2) + Hep(3) = 1 + 7 + 18 = 26 = (15/2)*1^2 + (21/2)*1 + 8.

a(2) = Hep(2) + Hep(3) + Hep(4) = 7 + 18 + 34 = 59 = (15/2)*2^2 + (21/2)*2 + 8.

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {8, 26, 59}, 50] (* Vincenzo Librandi, Feb 12 2012 *)

PROG

(MAGMA) I:=[8, 26, 59]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 20 2012

(PARI) a(n)=3*n*(5*n+7)/2+8 \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

Cf. A000566, A007667, A034961, A129803, A129863.

Sequence in context: A005897 A215097 A111694 * A002413 A218325 A252870

Adjacent sequences:  A129108 A129109 A129110 * A129112 A129113 A129114

KEYWORD

nonn,easy

AUTHOR

Jonathan Vos Post, May 24 2007

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 12 13:52 EST 2018. Contains 318063 sequences. (Running on oeis4.)