|
| |
|
|
A129111
|
|
Sums of three consecutive heptagonal numbers.
|
|
0
| |
|
|
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; internal format)
|
|
|
|
OFFSET
| 0,1
|
|
|
COMMENTS
| Arises in heptagonal number analogue 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.
|
|
|
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.
|
|
|
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.
|
|
|
CROSSREFS
| Cf. A000566, A007667, A034961, A129803, A129863.
Sequence in context: A085690 A005897 A111694 * A002413 A163121 A002901
Adjacent sequences: A129108 A129109 A129110 * A129112 A129113 A129114
|
|
|
KEYWORD
| easy,nonn
|
|
|
AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), May 24 2007
|
| |
|
|
