A221912 Partial sums of floor(n/12).

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 125, 130, 135, 140, 145, 150, 155

Offset

0,14

Comments

Apart from the initial zeros, the same as A008730.

Links

Table of n, a(n) for n=0..66.

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,0,0,0,0,1,-2,1).

Formula

a(12n) = A051866(n).

a(12n+1) = A139267(n).

a(12n+2) = A094159(n).

a(12n+3) = A033579(n).

a(12n+4) = A049452(n).

a(12n+5) = A033581(n).

a(12n+6) = A049453(n).

a(12n+7) = A033580(n).

a(12n+8) = A195319(n).

a(12n+9) = A202804(n).

a(12n+10) = A211014(n).

a(12n+11) = A049598(n).

G.f.: x^12/((1-x)^2*(1-x^12)).

a(0)=0, a(1)=0, a(2)=0, a(3)=0, a(4)=0, a(5)=0, a(6)=0, a(7)=0, a(8)=0, a(9)=0, a(10)=0, a(11)=0, a(12)=1, a(13)=2, a(n)=2*a(n-1)- a(n-2)+ a(n-12)- 2*a(n-13)+ a(n-14). - Harvey P. Dale, Mar 23 2015

Example

..0....0....0....0....0....0....0....0....0....0....0....0
..1....2....3....4....5....6....7....8....9...10...11...12
.14...16...18...20...22...24...26...28...30...32...34...36
.39...42...45...48...51...54...57...60...63...66...69...72
.76...80...84...88...92...96..100..104..108..112..116..120
125..130..135..140..145..150..155..160..165..170..175..180
186..192..198..204..210..216..222..228..234..240..246..252
259..266..273..280..287..294..301..308..315..322..329..336
344..352..360..368..376..384..392..400..408..416..424..432
441..450..459..468..477..486..495..504..513..522..531..540
...

Mathematica

Accumulate[Floor[Range[0, 70]/12]] (* or *) LinearRecurrence[{2, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -2, 1}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2}, 70] (* Harvey P. Dale, Mar 23 2015 *)

Crossrefs

Cf. A000217, A002620, A130518, A130519, A130520, A174709, A174738, A118729, A218470, A131242, A218530.

Sequence in context: A262358 A032962 A032519 * A008730 A033064 A246074

Adjacent sequences: A221909 A221910 A221911 * A221913 A221914 A221915

Keyword

nonn,tabf,easy

Author

Philippe Deléham, Mar 27 2013

Status

approved